May show equivalent or lower MWCO depending on solute and may be Influenced by operating conditions.

May show equivalent or lower MWCO depending on solute and may be Influenced by operating conditions.

Practical considerations, however, require a compromise between the ideal goals and process economics. One major factor is the lack of reliable information and/or molecular weight distribution of macrosolutes. As a result, application specialists or process engineers typically recommend a pore diameter which is about 75% of the smallest particle size or a MWCO value of about 50-60% lower than the smallest macrosolute. The objective is to maximize flux without sacrificing solute retention below the set minimum requirements.

Cross-Flow Velocity. The cross-flow velocity, which is also a measure of the shear or turbulence in the flow channels, may have a strong influence on flux. The actual shear or turbulence will depend on several factors such as channel diameter, viscosity and density of retentate and can vary over the duration of the filtration (especially for batch operations). This can be characterized by the calculation of Reynold's number on the reteníate stream. High Reynold's numbers (>4000) indicate turbulent flow whereas those below 2000 show laminar flow. The objective is to use a high cross-flow velocity to maximize flux by minimizing the gel polarization layer within the constraints imposed by the allowable pressure-drop or system limitations. It should also be noted that for many applications flux increases with cross-flow velocity. This is illustrated in Fig. 14.[21] The extent of flux improvement will depend on process stream, flow regime (laminar or turbulent) and characteristics of the gel polarization layer formed due to concentration buildup at the membrane/feed interface.^1

12 3 4

Cross-flow velocity, m/s

Figure 14. Effect of cross-flow velocity on flux. Yeast concentration, dry-g/L: (O) 8.5; (•>30.

Blatt et al.[20] have shown that the mass transfer coefficient can be related to the cross-flow velocity by

The value of k can be approximated by

The value of a can vary from 0.3 to 0.8 in laminar flow and 0.8 to 1.3 in turbulent flow. In the absence of particles (e.g., cells):

Eq. (4b) k oc v 0 6-0 8 (high particle loading) For turbulent flow:

This behavior has been explained by the so-called "tubular pinch effect," which enhances movement of particles away from the boundary layer thus reducing concentration polarization effect (see Sec. 3.3).

For turbulent flow, the pressure drop along the flow channel may be estimated by using the following empirical approximation:

Under laminar flow conditions,

This indicates that a higher cross-flow velocity under turbulent conditions can result in more than proportional increase in the pressure drop requiring larger pump discharge pressure to maintain a specified recirculation rate. This limits the number of modules that may be placed in series to minimize capital costs. Typical range of cross-flow velocity values is 2 to 7 m/s. The choice of pump is critical to obtain efficient fluid recirculation. It is critical to understand the shear sensitivity of the fluid/particle to be processed to determine the optimal cross-flow velocity in situations where shear-sensitive materials are involved.

Concentration of Solute or Particle Loading. It is essential to distinguish or separate the effects of membrane fouling from concentration polarization effects.

Membrane Fouling. Pretreatment of the membrane or feed solution prior to filtration may be desirable within allowable limits. The various treatment options are discussed in Sec. 6.3. At the start of a filtration run, the solute or solids concentration is relatively small and progressively builds as the permeate is removed from the system. If a substantial flux decline is observed at low solids concentration, membrane fouling aspects are believed to be important. A flux decrease with an increase in solids concentration is largely due to concentration polarization and can be minimized through efficient fluid hydrodynamics and/or backpulsing ,[3][22][231

Several approaches have been developed to control membrane fouling. They can be grouped into four categories: (a) boundary layer control;[201t241~[26] (b) turbulence inducers/generators;[27] (c) membrane modifications;1281"'301 and (d) use of external fields.[31H34] In CFF membrane, fouling can be controlled utilizing a combination of the first three approaches (a, b and c). The external field approach has the advantage of being independent of the hydrodynamic factors and type of membrane material.1351

Membrane fouling is primarily a result of membrane-solute interaction.'361 These effects can be accentuated or minimized by proper selection of membrane material properties such as hydrophobicity/hydrophilicity or surface charge, adjustment of pH, ionic strength and temperature leading to solubilization or precipitation of solutes. Increased solubilization of a foulant will allow its free passage into the permeate. If this is undesirable, precipitation techniques may be used which will enhance the retention of foulants by the membranes. Membrane fouling is generally irreversible and requires chemical cleaning to restore flux.

It is important to recognize that fouling in bioprocessing differs from that occurring with chemical foulants. Biofouling originates from microorganisms. Microbes are alive and they actively adhere to surfaces to form biofilms. Thus, in addition, to flux decrease there may be significant differences in solute rejection, product purity, irreversible membrane fouling resulting in reduced membrane life. For economic viability of CFF it is imperative that a good and acceptable cleaning procedure is developed to regenerate fouled membranes without sacrificing membrane life.

Concentration Polarization. The concentration of the species retained on the membrane surface or within its porous structure is one of the most important operating variables limiting flux. Concentration effects in MF/UF can be estimated by using the following most commonly used correlation, t121'371

310 Fermentation and Biochemical Engineering Handbook where

J - flux k = mass transfer coefficient

Cg = gel concentration of at the membrane surface

Cb = bulk concentration of solute retained by the membrane

In membrane filtration, some components (dissolved or particulate) of the feed solution are rejected by the membrane and these components are transported back into the bulk by means of diffusion. The rate of diffusion will depend on the hydrodynamics (laminar or turbulent) and on the concentration of solutes. If the concentration of solute at the surface is above saturation (i.e., the solubility limit) a "gel" is formed. This increases the flow resistance with consequential flux decrease. This type of behavior, for example, is typical of UF with protein solutions.

In practice, however there could be differences between the observed and estimated flux. The mass transfer coefficient is strongly dependent on diffusion coefficient and boundary layer thickness. Under turbulent flow conditions particle shear effects induce hydrodynamic diffusion of particles. Thus, for microfiltration, shear-induced diffusivity values correlate better with the observed filtration rates compared to Brownian diffusivity calculations.[5] Further, concentration polarization effects are more reliably predicted for MF than UF due to the fact that macrosolutes diffiisivities in gels are much lower than the Brownian diffusivity of micron-sized particles. As a result, the predicted flux for ultrafiltration is much lower than observed, whereas observed flux for microfilters may be closer to the predicted value.

Typically MF fluxes are higher than those for UF due to their higher pore diameter values which contribute to higher initial fluxes. However, polarization effects dominate and flux declines with increase in concentration (or % recovery) more sharply in MF than in UF, in general accordance with Eq. (4) under otherwise similar conditions. Figure 15 shows the typical dependence of flux on concentration.'141 Higher the concentration of the retained species on the membrane compared with its initial value, the higher will be % recovery. However, if the desired product is in the permeate, then % recovery will be dependent on the ratio of the batch volume to its final value for batch filtration or the ratio of concentrate in permeate to that in the feed for continuous filtrations.[38][391

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